This application relates generally to sofas and more particularly to a sofa that is convertible for use as a bed. Devices that are useful for seating but convertible for use as beds, are well known. Various approaches have been taken to accomplish this. One such approach is to combine conventional cushions with a conventional mattress in a seating unit, with the mattress folded up under the cushions. Another approach is to use cushions for seating and an air mattress for sleeping. It is difficult to combine the features of furniture seating comfort of a sofa and the sleeping comfort of a single purpose bed, in a unit occupying minimal floor space as a seating unit and without the need for space for separately storing seat cushions when used as a bed, or bedding when used as a sofa. In addition, where the sofa is to be used in a recreational vehicle or a mobile home, there are constraints on size and shape. This involves getting the sofa through a doorway and around one or more corners, and placing it at a suitable location in the vehicle. The present invention is addressed to dealing with some such problems.